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Perplexity 1600 1400 1200 1000 800 600 400 200 0 100 200 300 400 500 600 Sorted chunks Held-out set Eval set Figure 6.2: Perplexity of data chunks sorted by their performance on the development data. about 318M tokens 3 . In Figure 6.3, we show three variants of training the RNN LM: training on all concatenated training corpora with the natural order, standard stochastic gradient descent using all data (randomized order of sentences), and training with the reduced and sorted set. We can conclude that stochastic gradient descent helps to reduce the number of re- quired training epochs before convergence is achieved, against training on all data with the natural order of sentences. However, sorting the data results in significantly lower final perplexity on the development set - we observe around 10% reduction of perplexity. In Table 6.2, we show that these improvements carry over to the evaluation set. 6.5 Experiments with large RNN models The perplexity of the large 4-gram model with modified Kneser-Ney smoothing (denoted later as KN4) is 144 on the development set, and 140 on the evaluation set. We can see in Table 6.2 that RNN models with 80 neurons are still far away from this performance. 3 Training a standard n-gram model on the reduced set results in about the same perplexity as with the n-gram model that is trained on all data. 78
Perplexity 360 340 320 300 280 260 240 220 200 180 0 2 4 6 8 10 12 14 Epoch ALL-Natural ALL-Stochastic Reduced-Sorted Figure 6.3: Perplexity on the development set during training of RNN models with 80 neurons. In further experiments, we have used RNN models with increasing size of the hidden layer, trained on the Reduced-Sorted data set. We have used just 7 training epochs, as with sorted data, the convergence is achieved quickly (for the first three epochs, we used constant learning rate 0.1, and halved it at start of each new epoch). These results are summarized in Table 6.3. We denote RNN model with 80 neurons as RNN-80 etc. In Figure 6.4, we show that the performance of RNN models is strongly correlated with the size of the hidden layer. We needed about 320 neurons for the RNN model to match the performance of the baseline backoff model. However, even small models are Table 6.2: Perplexity on the evaluation set with differently ordered training data, for RNN models with various sizes of the hidden layer. Model Hidden layer size 10 20 40 80 ALL-Natural 357 285 237 193 ALL-Stochastic 371 297 247 204 Reduced-Sorted 347 280 228 183 79
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VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ
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Abstrakt Statistické jazykové mod
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Contents 1 Introduction 4 1.1 Motiv
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6.2.3 Reduction of Vocabulary Size
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Maybe the most popular vision of fu
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Chapter 6 presents further extensio
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Chapter 2 Overview of Stati
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2.1 Evaluation 2.1.1 Perplexity Eva
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ALP can be used to obtain prior pro
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• Good theoretical motivation •
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abilities of n-grams are stored in
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main (static) n-gram model. As the
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There are many popular examples sho
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y Chen et al., who proposed a so-ca
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confusion among researchers, and ma
Page 31 and 32: language model took almost a week u
Page 33 and 34: w(t) s(t-1) s(t) U V W y(t) Figure
Page 35 and 36: ate is halved at start of every new
Page 37 and 38: or using matrix-vector notation as
Page 39 and 40: information for more than 5 time st
Page 41 and 42: A simple solution to the exploding
Page 43 and 44: output layer changes to computation
Page 45 and 46: While RNN models can overcome this
Page 47 and 48: complex or random architectures (su
Page 49 and 50: While for any of the previous point
Page 51 and 52: where λ is the interpolation weigh
Page 53 and 54: model with default SRILM cutoffs pr
Page 55 and 56: experiments, we have used the one i
Page 57 and 58: Perplexity (Penn corpus) 145 140 13
Page 59 and 60: with syntactical NNLMs would be pre
Page 61 and 62: Table 4.3: Combination of individua
Page 63 and 64: Table 4.6: Results on Penn Treebank
Page 65 and 66: 4.6 Conclusion of the Model Combina
Page 67 and 68: were: 400 classes, hidden layer siz
Page 69 and 70: Entropy per word on the WSJ test da
Page 71 and 72: Table 5.3: Results on the WSJ setup
Page 73 and 74: Table 5.5: Results for models <stro
Page 75 and 76: trained together with a maximum ent
Page 77 and 78: wt-3 wt-2 wt-1 D D D P(wt|context)
Page 79 and 80: n-gram probabilities. However, it w
Page 81: Table 6.1: Training corpora for NIS
Page 85 and 86: Entropy per word 9 8.5 8 7.5 7 6.5
Page 87 and 88: 1 a a a 1 2 3 P(w(t)|*) ONE TWO THR
Page 89 and 90: Table 6.4: Perplexity on the evalua
Page 91 and 92: Entropy reduction per word over KN4
Page 93 and 94: Table 6.6: Perplexity with the new
Page 95 and 96: Entropy reduction over KN5 -0.04 -0
Page 97 and 98: as a baseline, and 12.3% after resc
Page 99 and 100: Table 7.1: BLEU on IWSLT 2005 Machi
Page 101 and 102: Table 7.3: Size of compressed text
Page 103 and 104: Table 7.4: Accuracy of different la
Page 105 and 106: Table 7.6: Entropy on PTB with n-gr
Page 107 and 108: 8.1 Machine Learning One possible d
Page 109 and 110: that almost every non-trivial compu
Page 111 and 112: supervision such as one digit at a
Page 113 and 114: Chapter 9 Conclusion and Future Wor
Page 115 and 116: from the expensive part of the mode
Page 117 and 118: Bibliography [1] A. Alexandrescu, K
Page 119 and 120: [23] D. Filimonov, M. Harper. A joi
Page 121 and 122: [50] T. Mikolov, S. Kombrink, L. Bu
Page 123 and 124: [77] W. Wang, M. Harper. The SuperA
Page 125 and 126: Test Phase After the model is train
Page 127 and 128: • compute sentence-level scores g
Page 129 and 130: Appendix B: Data generated from mod
Page 131 and 132: Appendix C: Example of decoded utte
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AND SAYS THIS SWING IS WITHIN A REA
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